Question: Simplify the following expression: $x = \dfrac{11t - 11}{-44t - 66}$ You can assume $t \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $11t - 11 = (11 \cdot t) - (11)$ The denominator can be factored: $-44t - 66 = - (2\cdot2\cdot11 \cdot t) - (2\cdot3\cdot11)$ The greatest common factor of all the terms is $11$ Factoring out $11$ gives us: $x = \dfrac{(11)(t - 1)}{(11)(-4t - 6)}$ Dividing both the numerator and denominator by $11$ gives: $x = \dfrac{t - 1}{-4t - 6}$